Checks or restrains without use of mystic arts (5)

I believe the answer is:

reins

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'checks' is the definition.
(reining is a kind of checking)

I can't explain the rest of the clue.

(Other definitions for reins that I've seen before include "Straps to control" , "Control for horses" , "Harnesses" , "water regulators?" , "Power to direct and control" .)

I've seen this clue in the Evening Standard.

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